A219357 a(n) = smallest number greater than n, equal to the determinant of the circulant matrix formed by its base-n digits.

17298, 1352, 28, 28, 320, 81, 133, 104, 247, 126, 1273, 252, 793, 473, 520, 980, 832, 513, 468, 5792, 684, 1738, 2511, 684, 1520, 14711, 7588, 938, 3857, 2275, 4680, 13392, 5184, 1648, 10535, 1820, 9143, 8473, 3843, 21880, 11609, 3843

Offset: 2

Author

Hans Havermann, Nov 18 2012

Keywords

• nonn
• base

Comments

Trivially all one-digit matrices are solutions, which is why 'greater than n' is specified. Two-digit matrices can never be a solution, so entries are actually greater than n^2. Most terms are three-digit solutions (less than n^3). Known exceptions are 15 digits (base 2), 7 digits (base 3), and 4 digits (bases 6, 798, 1182).

Up to base 1200, coincident terms are 28, 684, 3843, 8190, 47664, 80199, 351819, 323505, 5879259, 601524, 17159660, 20777715, respectively for base pairs (4,5), (22,25), (40,43), (81,86), (94,97), (112,115), (184,187), (276,386), (472,475), (738,749), (1061,1066), (1131,1136).

Examples

			In A219325 (base 2), the smallest number greater than 2 is 17298.
In A219324 (base 10), the smallest number greater than 10 is 247.
		

Links

• Hans Havermann, Table of n, a(n) for n = 2..1200
• Hans Havermann, log plot to base 1200
• Eric W. Weisstein, MathWorld: Circulant Matrix

Crossrefs

Cf. A219324 (base 10), A219325 (base 2).

Programs

Mathematica

dcm[n_,b_] := (l = IntegerDigits[n,b]; Det[NestList[RotateRight, l, Length[l]-1]]); Table[i=b; While[dcm[i,b] != i, i++]; i, {b, 2, 43}]